Churchlands, Representational Disconcert via State-Space Physics & Phase-Space Mathematics

If Paul Churchland delves in vectorialism and vector coding, Patricia Churchland and Terrence Sejnowski take a sojourn into state-space physics and phase mathematics. This is to define a particular state a network is in by mapping it to a point. This has the disconcerting effect of lending specificity to the point thus mapped, and obviously misses out on the all important relationship between parameters, and sub-spaces. This leap into the state-space physics and phase space mathematics is further disconcerting, for we lag behind in our intuitive qualities in visualizing higher-dimensions spaces. Even if, we humans lag behind in visualizing the number of higher dimensions, we are capable of working this out through algebraic representations. Through this algebraic representation, the utility of the state-space description is found to be to our taste, with a caveat being the diagrams’ proclivity to slide into a basin of attraction or converge onto a point with increasing complexity. Irrespective of the higher-dimensional predicaments, Churchlands take the seriousness of connectionism right to the heart of their models, and despite their clinging on to representation, make it very clear that representation as treated in connectionism is a far cry from the way it is traditionally understood.

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